In the case of your laptop there won't be any Windows 7 drivers. It has the ATI Mobility Radeon X1350, which along with everything else below the HD 2xxx series doesn't have any Windows 7 drivers due to ATI declaring them legacy status.
That said there are a couple of things you can try,
1. Try installing the XP driver from HP using compatibility mode, Compatibility Mode
2. Try the legacy driver, ATI Catalystâ„¢ Legacy Display Driver
Which may or may not install without some help. If it does install then there is nothing else to do. If it doesn't then you will need to use this, Mobility Modder - ATI Version, Install the Latest Drivers on your ATI laptop
to mod the driver so that it will install.